1. Field of the Invention
This invention relates to a method and system for generating a trajectory of a robot and the like, more particularly to a method and system for easily generating the trajectory of the leg (feet) of a legged mobile robot or other such trajectories wherein the contact between the leg (feet) and the ground and other such constraint conditions in its motion vary.
2. Description of the Prior Art
Trajectories are generated for use in the control of various kinds of moving objects, space rockets being a well-know example. Trajectory generation is also used in the control of robots, which have been proposed in stationary, mobile and other types. For example, Japanese Laid-open Patent Publication No. 3(1992)-248,207 teaches a trajectory generation of a distal end of a robotic arm, in which a smooth and continuous trajectory is generated by combining first and second acceleration/deceleration patterns in such a manner that the second pattern's acceleration is started before the first pattern ends while the second pattern's deceleration is suspended until the first pattern ends.
The reference relates to a stationary robot. For easier understanding, the invention will be explained with respect to a legged mobile robot of the biped locomotion type. Since a biped walking robot moves by alternately kicking against the ground with its two legs while at the same time supporting its own weight, the constraint conditions differ between the time of footrise and the time of footfall. This is shown in FIG. 12. At footrise the leg trajectory is constrained so that the leg rotates about the toe, while at footfall it is constrained so that it rotates about the heel. For defining the leg trajectory it is necessary to define the angle and position of, for example, the ankle joint. Although FIG. 12 indicates the position (displacement) of the ankle joint, for generating a smooth trajectory it is necessary to define the displacement, displacement velocity, displacement acceleration, angle, angular velocity and angular acceleration thereof. In such cases, the trajectory in space has conventionally been generated using a sixth-order polynomial. In cases where the constraint conditions differ between footrise and footfall, for example, it has therefore been necessary to solve the boundary conditions (boundary value problem) in order to obtain a smooth connecting trajectory. The amount of computation required for this, which is considerable even during straight walking on level ground, increases sharply when the ground is inclined and becomes extremely large during turning and the like. In the prior art, therefore, the computation is conducted in advance and the result stored in a memory of a microcomputer mounted on the robot. Therefore, when the robot encounters unexpected ground irregularities, slopes or obstacles, it cannot correct the trajectory in real time.